## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation. Let's define the variables and the objective function, as well as the constraints.

### Variables
- $x_1$ = Number of apple smoothies
- $x_2$ = Number of orange smoothies

### Objective Function
The objective is to maximize profit. Given that the profit per apple smoothie is $3.5 and per orange smoothie is $4.5, the objective function can be written as:
\[ \text{Maximize:} \quad 3.5x_1 + 4.5x_2 \]

### Constraints
1. Cutting machine constraint: $6x_1 + 5x_2 \leq 500$
2. Blending machine constraint: $3x_1 + 2x_2 \leq 500$
3. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'apple smoothies'), ('x2', 'orange smoothies')],
    'objective_function': '3.5*x1 + 4.5*x2',
    'constraints': [
        '6*x1 + 5*x2 <= 500',
        '3*x1 + 2*x2 <= 500',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

def solve_smoothie_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="apple_smoothies", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="orange_smoothies", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Objective function: Maximize 3.5*x1 + 4.5*x2
    model.setObjective(3.5 * x1 + 4.5 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(6 * x1 + 5 * x2 <= 500, name="cutting_machine_constraint")
    model.addConstr(3 * x1 + 2 * x2 <= 500, name="blending_machine_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Maximum profit: {model.objVal}")
    else:
        print("The model is infeasible")

solve_smoothie_problem()
```